Wind disturbances and noise severely affect Unmanned Aerial Vehicles (UAV) when monitoring and finding faults in overhead power lines. Accordingly, we propose repetitive learning as a new solution for the problem. In particular, the performance of Iterative Learning Control (ILC) that are based on optimal approaches are examined, namely (i) Gradient-based ILC and (ii) Norm Optimal ILC. When considering the repetitive nature of fault-finding tasks for electrical overhead power lines, this study develops, implements and evaluates optimal ILC algorithms for a UAV model. Moreover, we suggest attempting a learning gain variation on the standard optimal algorithms instead of heuristically selecting from the previous range. The results of both simulations and experiments of gradient-based norm optimal control reveal that the proposed ILC algorithm has not only contributed to good trajectory tracking, but also good convergence speed and the ability to cope with exogenous disturbances such as wind gusts.